{"id":26962563,"url":"https://github.com/nickhnelsen/random-features-banach","last_synced_at":"2025-04-03T05:28:48.990Z","repository":{"id":227980868,"uuid":"772837648","full_name":"nickhnelsen/random-features-banach","owner":"nickhnelsen","description":"Code for the paper \"The Random Feature Model for Input-Output Maps between Banach Spaces\"","archived":false,"fork":false,"pushed_at":"2024-08-08T11:36:52.000Z","size":20676,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2024-08-08T13:45:56.395Z","etag":null,"topics":["fourier-neural-operator","functional-regression","infinite-dimensions","neural-operator","operator-learning","partial-differential-equations","random-features"],"latest_commit_sha":null,"homepage":"https://doi.org/10.22002/55tdh-hda68","language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/nickhnelsen.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null}},"created_at":"2024-03-16T02:47:30.000Z","updated_at":"2024-08-08T11:36:56.000Z","dependencies_parsed_at":"2024-03-16T05:41:10.815Z","dependency_job_id":null,"html_url":"https://github.com/nickhnelsen/random-features-banach","commit_stats":null,"previous_names":["nickhnelsen/random-features-banach"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/nickhnelsen%2Frandom-features-banach","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/nickhnelsen%2Frandom-features-banach/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/nickhnelsen%2Frandom-features-banach/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/nickhnelsen%2Frandom-features-banach/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/nickhnelsen","download_url":"https://codeload.github.com/nickhnelsen/random-features-banach/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":246943764,"owners_count":20858767,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["fourier-neural-operator","functional-regression","infinite-dimensions","neural-operator","operator-learning","partial-differential-equations","random-features"],"created_at":"2025-04-03T05:28:48.398Z","updated_at":"2025-04-03T05:28:48.964Z","avatar_url":"https://github.com/nickhnelsen.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# random-features-banach\nThis repository contains the code associated with the journal articles \"The Random Feature Model for Input-Output Maps between Banach Spaces\" ([SIAM J. Sci. Comput., Vol. 43, No. 5 (2021), pp. A3212–A3243](https://doi.org/10.1137/20M133957X)) and \"Operator learning using random features: a tool for scientific computing\" ([SIAM Review, Vol. 66, No. 3 (2024), pp. 535–571](https://doi.org/10.1137/24M1648703)). It implements the function-valued random features method for two operator learning benchmark problems: 1) the solution operator of 1D viscous Burgers' equation and 2) the solution operator of the 2D Darcy flow elliptic partial differential equation.\n\n\u003e [!IMPORTANT]  \n\u003e A more efficient and up-to-date GPU implementation of this code is available at:\n\u003e \n\u003e https://github.com/nickhnelsen/error-bounds-for-vvRF\n\u003e \n\u003e We recommend that users interested in the operator random features method migrate over to that repository. The current repo `random-features-banach` should only be used to reproduce the results in the journal papers and not used for future developements.\n\n## Requirements\n* Python 3\n* Numpy\n* Numba\n* Scipy\n* Matplotlib\n\n## Data\nThe data may be downloaded at [![DOI](https://data.caltech.edu/badge/DOI/10.22002/55tdh-hda68.svg)](https://doi.org/10.22002/55tdh-hda68), which contains two `*.zip` files:\n1. `burgers`: input-output data as Python `*.npy` files.\n2. `darcy`: input-output data as MATLAB `*.mat` files.\n\n```\nNelsen, N. H. \u0026 Stuart, A.M. (2024). Operator learning using random features: a tool for scientific computing [Data set]. CaltechDATA. https://doi.org/10.22002/55tdh-hda68. Mar. 15, 2024.\n```\n\n## References\nThe main reference that explains the two benchmark problems is the paper ``[The Random Feature Model for Input-Output Maps between Banach Spaces](https://arxiv.org/abs/2005.10224)'' by Nicholas H. Nelsen and Andrew M. Stuart. Other relevant references include:\n- [Error Bounds for Learning with Vector-Valued Random Features](https://arxiv.org/abs/2305.17170)\n- [Fourier Neural Operator for Parametric Partial Differential Equations](https://arxiv.org/abs/2010.08895)\n- [Operator learning using random features: a tool for scientific computing](https://doi.org/10.1137/24M1648703)\n\n## Citing\nIf you use `random-features-banach` in an academic paper, please cite the main references as follows:\n```\n@article{nelsen2021random,\n  title={The random feature model for input-output maps between Banach spaces},\n  author={Nelsen, Nicholas H. and Stuart, Andrew M.},\n  journal={SIAM Journal on Scientific Computing},\n  volume={43},\n  number={5},\n  pages={A3212--A3243},\n  year={2021},\n  publisher={Society for Industrial and Applied Mathematics},\n  doi = {10.1137/20M133957X}\n}\n\n\n@article{nelsen2024operator,\n\ttitle={Operator learning using random features: a tool for scientific computing},\n\tauthor={Nelsen, Nicholas H. and Stuart, Andrew M.},\n\tjournal={SIAM Review},\n\tvolume={66},\n\tnumber={3},\n\tpages={535--571},\n\tyear={2024},\n\tmonth={8},\n  publisher={Society for Industrial and Applied Mathematics},\n  doi={10.1137/24M1648703}\n}\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fnickhnelsen%2Frandom-features-banach","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fnickhnelsen%2Frandom-features-banach","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fnickhnelsen%2Frandom-features-banach/lists"}